(CBS/AP) NEW ORLEANS - Jury selection began Monday in a legal fight between two Hollywood stars over investments in a device used to try to clean up BP's 2010 oil spill in the Gulf of Mexico.

Actor Stephen Baldwin, center, arrives at Federal Court after a lunch break, in New Orleans, on June 4, 2012.
AP Photo/Bill Haber

In his lawsuit, actor Stephen Baldwin claims Kevin Costner and a business partner duped Baldwin and a friend out of their shares of an $18 million deal for BP to buy oil-separating centrifuges after the April 2010 spill.

U.S. District Judge Martin L.C. Feldman told prospective jurors they could not be influenced by the celebrity status of Baldwin and Costner. Both actors were in court. Costner wore a blazer and khakis, while Baldwin wore an olive suit.

"Celebrity has no place in this courtroom or in any of the issues that need to be resolved by the jury in this trial," Feldman said.

Feldman asked the potential jurors whether the entertainers' on-screen portrayals compromised the ability to deliver an objective verdict. No one in the pool said they would feel influenced.

Among Baldwin's roles was caveman Barney Rubble in "The Flintstones: Viva Rock Vegas." Costner's films include "Dancing with Wolves," "Field of Dreams," and "JFK," Oliver Stone's film with New Orleans connections to the assassination of President John F. Kennedy.

Baldwin and Costner did not interact before the proceedings started. Baldwin told The Associated Press his attorneys had advised him not to comment.

Baldwin and his friend, Spyridon Contogouris, said they didn't know about the deal when they agreed to sell their shares of Ocean Therapy Solutions, a company that marketed the centrifuges to BP, for $1.4 million and $500,000, respectively.

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BP ordered 32 of the centrifuges and deployed a few of the devices on a barge in June 2010. BP capped its blown-out Macondo well the following month and kept more oil from leaking until the well was permanently sealed in September 2010.

(At left, watch Costner testify to Congress about the machine in 2010)

Baldwin and Contogouris claim they were deliberately excluded from a June 8 meeting between Costner, his business partner Patrick Smith and BP executive Doug Suttles, who agreed to make an $18 million deposit on a $52 million order for the 32 devices, according to the lawsuit.

Later that month, Costner and Suttles visited Port Fourchon, La., to talk about the plan to use the centrifuges.

"It was designed to give us a fighting chance, to fight back the oil before it got us by the throat," Costner said at the time.

Baldwin and Contogouris say they were entitled to shares of BP's deposit. Their lawsuit claims Costner and Smith schemed to use BP's deposit buy their shares in Ocean Therapy Solutions.

"Maybe one of the directions that Mr. Costner might go as a defendant in this case is that he had taken a great deal of risk as it relates to these machines," legal analyst Chick Foret told WWL-TV.

Costner said he didn't attend a June 6, 2010, meeting at which Contogouris agreed to sell his OTS interests.

"Not only did Costner not know that Plaintiffs were negotiating to sell their OTS interests, he was surprised and offended by the idea that Contogouris and Baldwin would walk away from OTS with almost $2 million in cash despite having invested no money in the company, and at a time when a contract with BP was uncertain to materialize," says a court filing summarizing Costner's version of events.

Baldwin and Contogouris are seeking more than $21 million in damages. Costner and other defendants also are seeking damages in counterclaims.